A torsion damper of the kind described above (which will be referred to herein as a torsion damper of the kind specified) is described in French published Patent Application No. 2 597 181, in which one of the relatively moveable parts is adapted to be coupled with the driving shaft and the other with the driven shaft, in each case for rotation with the appropriate shaft, and the cavity is filled with fluid. Calibrated passages are provided, especially between the free end of a fin of one group and the carrying element associated with the fins of the other group. In order to reduce the damping effect when the engine is in a decelerating mode with the gearbox on dead centre, it is possible to use an arrangement of the same kind as that which is described in French published Patent Application No. 1 375 156, in which the dimensions of a transfer passage vary under the action of a progressively acting obturator which is incorporated in the fins or vanes associated with the outer carrying element. This obturator is in the form of a plunger, and is acted on by a return spring. The plunger extends through a transfer passage located at the foot of the appropriate vane. Such an arrangement is comparatively expensive, because, not only must the obturator be made to fit accurately, but also the manufacture of the transfer passages is a somewhat delicate operation. In addition, high precision calibrated passages exist in the vicinity of the free ends of the fins associated with the inner carrying element.